Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

2.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

3.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

4.Work out the value of a² − 2b when a = −3 and b = 4.

5.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

6.Write down 0.2x with its coefficient written as a fraction in its simplest form.

7.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

8.Make x the subject of the formula y = x + 7.

9.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

10.A square has sides of length y cm. Write down an expression for the perimeter of the square.

11.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

12.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

13.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

14.Which expression is equivalent to 6x − (2x − 5)?

15.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.